The global existence issue in critical spaces for compressible Navier-Stokes equations, was addressed by Danchin (2000) and then developed by Charve-Danchin (2010), Chen-Miao-Zhang (2010) and Hasport (2011) in more general L p setting. Our aim is to exhibit (more precisely) time-decay estimates of solutions constructed in the critical framework. As we known, the low-frequency assumption usually plays a key role in the large-time asymptotics of solutions, which was firstly observed in usual L 1 space by Matsumura and Nishida [30]. In this paper, we claim a new low-frequency assumption for barotropic compressible Navier-Stokes equations, which may be of interest in the mathematical analysis of viscous fluids. Precisely, if the initial density and velocity additionally belong to some Besov spaceḂ −σ 1 2,∞ with the regularity σ1 ∈ (1−d/2, 2d/p−d/2] , then a sharp time-weighted inequality including enough time-decay information can be available, where optimal decay exponents for the high frequencies are also exhibited. The proof mainly depends on tricky and non classical Besov estimates. As a by-product, those optimal time-decay rates of L q-L r type are well captured in the critical regularity framework.